The four fours.

[Amram]

time for a break.

Besides, 30 numbers in as many minutes is a good run.

i'll just put this back.....

140 = Γ(Γ(4)) + 4!! + Γ(4) + Γ(4)

and here I thought I was losing it, I saw 139, so i posted, and then, oh look, I replied to myself, wtf. So I pull my 140, only to find I did see it, and Chris has now gone on without me, lol. Yep, time to take a break.

Edited December 29, 2013 by Amram
I derped....

[Chrisd857]

I seem to have deleted my 139, so here it is with 141. Bed is soon here, too.

139 = A( √(!4), 4 ) + Γ(4) + 4!!

141 = A( √(!4), 4 ) + 4!! + 4!!

And Amram's 140 seems to have disappeared, so:

140 = Γ(Γ(4)) + 4!! + Γ(4) + Γ(4)

And I am done for today.

Edited December 29, 2013 by Chrisd857

[Amram]

chaos, thats what has ensued, lots of it.

[vexx32]

Chris, I restored your 139, hehe. I'm just gonna give you guys rep and leave before I get tempted to get caught up in all of this. Now is not the time for me to be doing math puzzles. :/

[Amram]

142 = Γ(Γ(4)) + 4!! + 4!! + Γ(4)

[Chrisd857]

143 = A( √(!4), 4 ) + Γ(4) * √(!4)

[Amram]

144 = Γ(Γ(4)) + 4!! + 4!! + 4!!

[Chrisd857]

145 = A( √(!4), 4 ) + Γ(Γ(4)) / Γ(4)

[Sesni]

Alright... 4^4x4^4

(^ means exponent)

So my calculators will not finish it.

But beat this. 4^1024.

Note : The area in parentheses is part of the exponent : 4^(4x4^4) Just want to make it not confusing.

[Chrisd857]

Alright... 4^4x4^4

(^ means exponent)

So my calculators will not finish it.

But beat this. 4^1024.

Note : The area in parentheses is part of the exponent : 4^(4x4^4) Just want to make it not confusing.

Well, the point was to count, not simply post a larger number.

146 = A( √(!4), 4 ) +4! + √(!4)

Edit: should be shown as 146 = A( √(!4), 4 ) +4! - √(!4) (the wolframalpha link is correct with the minus)

Edited January 6, 2014 by Chrisd857

[Amram]

But beat this. 4^1024.

done.

4^4^4^4 > 4^1024

FAR larger still:4!^4!^4!^4! > 4^4^4^4

The second one is basically 24^24^24^24, which is needless to say, HUGE. Yet i can go considerably large still.

((((4!)!)!)!)! = 10^(10^(10^(10^(10^1.400868540431458)))), which is WAY larger than even 4!^4!^4!^4!

So

((((4!)!)!)!)!^((((4!)!)!)!)!^((((4!)!)!)!)!^((((4!)!)!)!)!

Top that.

Yet its easy. Throw the entire thing in another set of parenthesis, and apply the factorial function, done.

(((((4!)!)!)!)!^((((4!)!)!)!)!^((((4!)!)!)!)!^((((4!)!)!)!)!)! is bigger, MUCH bigger.

The largest value one can reach is about as close to infinity as to be essentially impossible to conceive of. There's no limit on how many functions you can wrap those four fours in, which is why the challenge is not to reach the largest possible value in which case you could ALWAYS take the previous answer, wrap it in another set of parenthesis and then append a !, and its bigger, MUCH bigger. Given that, an infinite number of factorial operations , each operating on the answer to the previous operation as happens when each is in its own set of parenthesis, would essentially get you an infinitely large number, and that's that.

Of course you read the rules to the game before joining in said game, so you definitely saw Rule 6 right? Your number must be the next integer in sequence. So you'll be free to use that one sometime next millennium i think.

I would have thought 16 pages of sequential numbering would have made that rule redundant by now.

147 = A( √(!4), 4 ) +4! - √4

Edited January 8, 2014 by Amram
edit, derped on shown math, but the link was good.

[Chrisd857]

Amram - shouldn't it be -√4? Not +√4.

Which also means that my 146 should've been 146 = A( √(!4), 4 ) +4! - √(!4)

148 = A( √(!4), 4 ) +4! - !(√4)

[Amram]

yep, your correct, I had a good link to the right answer, just flubbed my text for the link, fixed.

149 = A( √(!4), 4 ) + 4!! * √(!4)

[Starwhip]

150 = (4! * 4!)/4 + Γ(4)

(Is Γ the thing that does what ! does, minus 1? As in Γ4 = 3*2*1)

[Amram]

yep, tested a couple values at wolframalpha to confirm.

1*2*3 = Γ(4) = 6

1*2*3*4 = Γ(5) = 24

1*2*3*4*5 = Γ(6) = 120 (which is why you'll find me doing Γ(Γ(4)) quite a bit, since its equivalent to Γ(6), which is 120. Useful at these numbers.

I think you understand it well enough, and put like that makes way more sense to me than how wolframalpha explains it, lol. I look at their definition page for gamma and my head explodes.

151 = Γ(Γ(4)) + 4! + Γ(4) + !(√4)

Edited January 10, 2014 by Amram
link fix, i've been on a roll lately

[Chrisd857]

152 = (A( √(!4), √4 ) + !4) * 4

[Amram]

153 = Γ(Γ(4)) + 4! + Γ(4) + √(!(4))

[Chrisd857]

154 = Γ(4) * 4! + 4!! + √4

[Amram]

155 = Γ(4) * 4! + 4!! + √(!(4))

[Chrisd857]

156 = Γ(Γ(4)) + 4 * √(!(4)) * √(!(4))

[Amram]

157 = 4! * Γ(4) + !4 + 4

[Chrisd857]

158 = Γ(Γ(4)) + Γ(4) * Γ(4) + √4

[Amram]

159 = 4! * Γ(4) + !4 + Γ(4)

[Chrisd857]

160 = 4 * 4 * ( !(√4) + !4)

[Amram]

161 = !4 * (!4 + !4) + !(√4)